Problem: Solve for $x$ and $y$ using elimination. ${4x+6y = 44}$ ${-x+5y = 2}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${4x+6y = 44}$ $-4x+20y = 8$ Add the top and bottom equations together. $26y = 52$ $\dfrac{26y}{{26}} = \dfrac{52}{{26}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {4x+6y = 44}\thinspace$ to find $x$ ${4x + 6}{(2)}{= 44}$ $4x+12 = 44$ $4x+12{-12} = 44{-12}$ $4x = 32$ $\dfrac{4x}{{4}} = \dfrac{32}{{4}}$ ${x = 8}$ You can also plug ${y = 2}$ into $\thinspace {-x+5y = 2}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(2)}{= 2}$ ${x = 8}$